% Upper bound of the second summand in analytical approximation of core function
% Usage: y = integ_check_for_K1_max_V(zeta, m, CONSTS)

function y = integ_check_for_K1_max_V(zeta, m, CONSTS)
    a = CONSTS.a;
    eps = CONSTS.eps;
    eta = CONSTS.eta;
    eps_a = CONSTS.eps_a;
    sigma = CONSTS.sigma;
    use_V = CONSTS.use_V;
    
    y_temp = - (m^2/((eps*eta)^0.5)) *          ...
        (log(sigma) + log(zeta/(2*a)) + 2*sum(1./(2*(1:abs(m))-1)) - ...
        2*log(2));
    if (use_V)
        y = y_temp * (((eps*eta)^0.5)/eps_a);
    else
        y = y_temp;
    end
end
